Casimir interaction of strained graphene

We calculate the Casimir interaction of two freestanding graphene samples under uniaxial strain. Our approach fully takes retardation and dispersion into account and is based on quantum field theoretical expressions for conductivities in terms of the polarization operator. The force shows a rather weak dependence on the realistic values of strain, changing just by a few percent in its maximum as compared to the non-strained case.Comment: 5 pages, 3 figures, EPL style, misprint correcte

Casimir energy of finite width mirrors: renormalization, self-interaction limit and Lifshitz formula

We study the field theoretical model of a scalar field in presence of spacial inhomogeneities in form of one and two finite width mirrors (material slabs). The interaction of the scalar field with the defect is described with position-dependent mass term. Within this model we derive the interaction of two finite width mirrors, establish the correspondence of the model to the Lifshitz formula and construct limiting procedure to obtain finite self-energy of a single mirror without any normalization condition.Comment: 5 pages, based on the presentation on the Ninth Conference on Quantum Field Theory under the influence of External Conditions, Oklahoma, 200

Zeroes of combinations of Bessel functions and mean charge of graphene nanodots

We establish some properties of the zeroes of sums and differences of contiguous Bessel functions of the first kind. As a byproduct, we also prove that the zeroes of the derivatives of Bessel functions of the first kind of different orders are interlaced the same way as the zeroes of Bessel functions themselves. As a physical motivation, we consider gated graphene nanodots subject to Berry-Mondragon boundary conditions. We determine the allowed energy levels and calculate the mean charge at zero temperature. We discuss in detail its dependence on the gate (chemical) potential.Comment: vesrion accepted to Theoretical and Mathematical Physics, 18 pages, 1 figur

Localized Solutions of the Non-Linear Klein-Gordon Equation in Many Dimensions

We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.Comment: 4 pages, 1 figur

Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons

We consider gated graphene nanoribbons subject to Berry-Mondragon boundary conditions in the presence of weak impurities. Using field--theoretical methods, we calculate the density of charge carriers (and, thus, the quantum capacitance) as well as the optical and DC conductivities at zero temperature. We discuss in detail their dependence on the gate (chemical) potential, and reveal a non-linear behaviour induced by the quantization of the transversal momentum.Comment: 17 pages, version accepted for publication in EPJ